Chapter 4 - Section 4.5 - Graphs of Sine and Cosine Functions - Exercise Set - Page 596: 51

Please see below.

Please note that a cosine function $y=A\cos (Bx-C)$ has amplitude $|A|$, period $\frac{2\pi }{B}$, and phase shift $\frac{C}{B}$. So the function $y=2\cos (2\pi x+8\pi )$ has amplitude $|2|=2$, period $\frac{2\pi }{2\pi }=1$, and phase shift $\frac{-8\pi }{2\pi }=-4$.